1, 9, 1, 89, 1, 9, 1, 889, 1, 9, 1, 89, 1, 9, 1, 8889, 1, 9, ...

start with the sequence of all decimal numbers with only the digits 0,1 and take their first differences.  i.e
0,1,10,11,100,101,110,111,1000,1001,1010,1011,....
1-0=1
10-1=9
11-10=1
100-11=89
101-100=1
110-101=9
111-110=1
1000-111=889
1001-1000=1
1010-1001=9
1011-1010=1
.......